A force of 3.24 x 10^-12 N exists between a +3 charge and another charged particle. The ions are 2.53 x 10^-8 m apart. What is the charge of the unknown charged particle?  (Rework numbers since you went from +15 to +3)

• A. 4.79 x 10^-19 C
• B. 7.59 x 10^-18 C
• C. 5.89 x 10^-18 C
• D. 4.12 x 10^-19 C

Answer: (A)

Verified step by step guidance

1. Identify the formula to use: The force between two charges can be calculated using Coulomb's Law, which is given by the equation: $F=\frac{k{q}_1{q}_2}{r^2}$, where $F$ is the force, $k$ is Coulomb's constant ($8.99\; \times \; 109N\; m2/C2$), $q_1$ and $q_2$ are the charges, and $r$ is the distance between the charges.
2. Rearrange the formula to solve for the unknown charge $q_2$: $q_2=\frac{F{r}^2}{k{q}_1}$.
3. Substitute the known values into the rearranged formula: $F=\; 3.24\; \times \; 10-12N$, $r=\; 2.53\; \times \; 10-8m$, $q_1=\; 3$ (since the charge is +3).
4. Calculate the square of the distance: $r^2=\; (2.53\; \times \; 10-8m)2$.
5. Plug the values into the formula and solve for $q_2$: $q_2=\frac{(3.24\; \times \; 10-12N)\; \times \; (2.53\; \times \; 10-8m)2}{(8.99\; \times \; 109N\; m2/C2)\; \times \; 3}$.